Students will write equations that correspond to given situations and use formulas to solve problems. Students will learn that solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will also construct and analyze tables, such as quantities that are in equivalent ratios, and use equations to describe relationships between quantities. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Ideas
Determine if an equation or inequality is appropriate for a given situation
Represent and solve mathematical and real world problems with equations and inequalities
Interpret the solutions to equations and inequalities
Represent the solutions to inequalities on a number line
Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs
Essential Questions
How can students use substitution to make an equation true?
How can students use variables to represent numbers?
How can students show that a variable can represent an unknown number?
How can students solve word problems with equations?
How can students solve inequalities?
How can students dependent and independent variables?
Vocabulary
Addition Property of Equality: Adding the same number to each side of an equation produces an equivalent expression.
Constant of proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the constant of proportionality. In a proportional relationship, y = kx, k is the constant of proportionality, which is the value of the ratio between y and x.
Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: A=kB, where k is the constant of proportionality.
Division Property of Equality: States that when both sides of an equation are divided by the same number, the remaining expressions are still equal
Equation: A mathematical sentence that contains an equal sign
Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤.
Inverse Operation: A mathematical process that combines two or more numbers such that its product or sum equals the identity.
Multiplication Property of Equality: States that when both sides of an equation are multiplied by the same number, the remaining expressions are still equal.
Proportion: An equation which states that two ratios are equal.
Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.
Term: A number, a variable, or a product of numbers and variables.
Variable: A letter or symbol used to represent a number or quantities that vary
Content
Students will determine if an equation or inequality is appropriate for a given situation
Students will represent and solve mathematical and real world problems with equations and inequalities
Students will interpret the solutions to equations and inequalities
Students will represent the solutions to inequalities on a number line
Students will analyze the relationship between dependent and independent variables through the use of tables, equations and graphs
Skills Needed
Using parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Write and interpret numerical expressions.
Generating two numerical patterns using two given rules.
Interpret a fraction as division
Operations with whole numbers, fractions, and decimals
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Table of Contents
Common Core Learning Standard
Big Ideas
Essential Questions
Vocabulary
Content
Skills Needed
Arc 1 Equations
6.EE.7
1-Step Equations
2-Step Equations
3-3
3-4
3-5
3-6
3-7
5-6
6-5
12-1
12-2
12-3
143-173
534-545
546-559
560-572
Changing Quantities
Dependent and Independent Variables
CC13
137 #32-35
139 #40
141 #52
142 #55
143-173
468-488
489-508
552-554
556-559
Assessments
Arc 2 Inequalities
12-3
546-559
572
Assessment
Unit Assessments
6.EE.5
- Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.6- Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7- Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.8- Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
6.EE.9